Nonuniform heating of a substrate in evaporative lithography

Abstract

This work is devoted to a method to generate particle cluster assemblies and connected to evaporative lithography. Experiments are carried out using nonuniform evaporation of an isopropanol film containing polystyrene microspheres in a cylindrical cell. The local inhomogeneity of the vapor flux density is achieved by exploiting the temperature gradient. A copper rod is mounted in the central part of the bottom of the cell for further heating. The thermocapillary flow resulting from the surface tension gradient, due in turn to the temperature drop, transfers the particles that were originally at rest at the bottom of the cell. The effect of the initial thickness of the liquid layer on the height and base area of the cluster formed in the central region of the cell is studied. The velocity is measured using particle image velocimetry. A model describing the initial stage of the process is developed. The equations of heat transfer and thermal conductivity are used to define the temperature distribution in the liquid and in the cell. The fluid flow is simulated using the lubrication approximation. The particle distribution is modeled using the convection–diffusion equation. The evaporation flux density is calculated using the Hertz–Knudsen equation. The dependence of the liquid viscosity on the particle concentration is described by Mooney's formula. Numerical results show that the liquid film gradually becomes thinner in the central region, as the surface tension decreases with the increasing temperature. The liquid flow is directed to the heater near the substrate, and it transfers the particles to the center of the cell. The volume fraction of the particles increases over time in this region. The heat flow from the heater affects the geometry of the cluster for two reasons: First, the Marangoni flow velocity depends on the temperature gradient, and second, the decrease in film thickness near the heater depends on the temperature. The results of the simulation are in general agreement with the experimental data.

Influence of fluid flows on electric double layers in evaporating colloidal sessile droplets

“…6). This is natural if the adhesion to the substrate and capillary attraction between the particles are not taken into account [13,45,46]. Nevertheless, Fig.…”

Circulating Marangoni flows within droplets in smectic films

“…where c 3 and c 4 are also the integration constants. After substitution of expressions (12,13) to Eq. ( 11) we obtain c 1 = c 3 .…”

“…An extensive literature on thermocapillary driven flows in fluid films exists and both experimental and theoretical studies are thoroughly reviewed; see for example [7][8][9][10]. The Marangoni phenomenon is important not only for development of fundamental physics of capillarity and wetting; it is frequently encountered in industrial applications, including chemical engineering, food and cosmetic processing, thermal management of micro-fluidic and electronic devices, evaporation related technology [6,[10][11][12]. The role of Marangoni convection is especially important in thermal processing of electronic and rheological devices in microgravity conditions where buoyancy effects are negligible [13][14][15].…”

Numerical Simulation of Thermocapillary Convection with Evaporation Induced by Boundary Heating

“…The mechanism of occurrence of convective motion is related to changes in the surface tension of a liquid. The changes can result from an external thermal action [1,2], concentration effects [3][4][5] or evaporation [6][7][8] on the liquid surface. If the combined action of these effects occurs, they can be amplified or they can compete with each other, causing the alteration of flow regimes and instabilities of different nature.…”